A particle of mass m is moving yz- plane with a uniform velocity v with its trajectory running parallel to $+\text{ve}$  y-axis and intersecting z- axis at $\text{z}=\text{a}$  . The change in its angular momentum about the origin as it bounces elastically from a wall at $\text{y}=\text{constant}$  is

The initial velocity is${\text{v}}_i=\text{v}{\hat{e}}_y$  and after reflection from the wall, the final velocity is ${\text{v}}_f=-\text{v}{\hat{e}}_y$ .

The trajectory is at constant distance ‘a’ on z axis and as particles moves along y axis, its ‘y’ component changes so position vector (moving along y – axis) $\overline{r}=y{\hat{e}}_y+a{\hat{e}}_{\text{z}}$

Hence, the change in angular momentum is$\overline{r}\times \text{m}\left(v_f-v_i\right)$

$=2\text{mva}\hat{e}x\left(\hat{e}x=\hat{i}\right)$

$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ \text{mva}& 0& 0\\ -\text{mva}& 0& 0\end{array}\right|\Rightarrow \hat{i}(\text{mva}-\left(-\text{mva}\right)\Rightarrow \left(2\text{mva}\right)\uparrow$